Question

Prove that if m + n and n + p are even integers, where m, n and p are integers, then m + p is even

Answer 1

i suppose first step would be to assume m+n and n+p are even...

Answer 2

so

m + n = 2k

n + p = 2x

Answer 3

then i suppose i solve for n...

Answer 4

n = 2k - m

n = 2x - p

Answer 5

then i suppose i equate them

2k - m = 2x - p

Answer 6

then i suppose this happens

2k - 2x = m - p

Answer 7

then if i factor out...

2 (k - x) = m - p

Answer 8

so... m - p is even

but how do i prove m + p is even?

Answer 9

m+n = 2x
n+p = 2y
add them and see whether u can proceed with the proof

Answer 10

ahh yes.. i see it